A Linear interferometer direction finding (DF) antenna array may be utilized for 1) reception of Radio Frequency (RF) signals from an emitter, and 2) for determining the bearing to the signal based on an analysis of a phase shift between the signals received by the separate antennas comprising the array. For example, signals transmitted from a radar emitter or communication emitter may propagate in a plurality of directions. Each antenna of a linear interferometer array may receive the signal in order to determine from which direction the signal is being emitted relative to the receiving antenna array. A standard class of algorithm may then be used to receive an input from the array to calculate a bearing from receiver to the emitter. The standard algorithm may use well known techniques to achieve the bearing.
A Linear Interferometer may comprise multiple antennas positioned to provide multiple antenna-to-antenna baselines for measuring differences in electrical phase of an arriving RF signal. The length of the baselines, herein referred to as the spacing, may be the basis for a plurality of calculations made by the standard algorithm. In a conventional precision linear interferometer, each of these baselines may be significantly longer than the ½λ (lambda). Herein λ may be defined as the wavelength of the antenna array's highest operating frequency.
A ½λ antenna spacing may provide a one-to-one mapping of arrival angle across +/−90 mechanical degrees to +/−90 degrees of electrical phase measurements. With longer antenna spacing, (greater than ½λ) the +/−90 mechanical degrees map to more than +/−90 electrical degrees and cannot be unambiguously resolved. For example, ambiguity may arise where multiple arrival angles result in the same electrical phase measurement as an algorithm may rely on the phase measurement as an input variable to the DF determination. In precision DF arrays, multiple elements (3 or more) may be arranged to provide multiple baselines (2 or more) such that each arrival angle may map to a unique combination of the multiple phase measurements.
Using multiple baselines may allow use of much longer antenna spacing than ½λ. Current precision interferometers may use a standard spacing from 10 to 25λ or more. Additionally, considerably longer antenna spacing of greater than 60λ has been investigated and determined to provide accurate DF measurements. One advantage of a longer baseline may include improved DF accuracy. The improvement in DF accuracy may be directly proportional to the increase in the antenna baseline. For example, a baseline length 20λ may provide a 40 fold increase in accuracy over what could be achieved with a ½λ spacing. Multiple antenna linear interferometer arrays working in unison may provide for even greater DF accuracy. However, implementation of such longer spacing and multiple arrays may present a challenge.
These longer baselines and multiple arrays, however, present a current challenge of allowable space on an airframe or platform to which the antenna array may be mounted. An aircraft designer may not have available the required physical distance to generate the accuracy provided by such longer baselines.
Additionally, various methods of determining a DF solution based on measured phase values may result in the generation of ambiguous DF solutions, or invalid DF solutions, at low signal to noise ratios.
A closed form method of analysis of measured values may be currently in use in a variety of systems. This closed form method may be implemented in real time systems in a variety of ways. Early implementations used ROM look-up tables incorporated in the algorithm. Current implementations may utilize Field Programmable Gate Arrays (FPGAs) to implement the algorithm in a manner very close to the way it may be written in algebraic form. Both implementations may be used to calculate DF solutions to a high level of accuracy within a few hundred nanoseconds. Calculation speed may of considerable importance for real time systems that intercept and process millions of signals per second. One advantage of the FPGA approach may include flexibility and reduced development time. This closed form approach may also have been implemented in software. Software implementations however, may be limited to systems that calculate DF on only a small subset of intercepted signals.
One drawback of the closed form approach may be encountered when a significant amount of error is included in the phase measurements due to low signal to noise ratio (SNR). With a certain amount of error, the closed form algorithm may calculate the wrong integer and may generate the wrong DF solution. This type of DF error may be referred to as ambiguity. Closed form algorithms may be structured so that the possibility of such ambiguity may be indicated. However, when such an ambiguity condition exists, the closed form algorithm provides no alternate solution. The result of such an error may be of two types: 1) where a valid but wrong DF angle is generated, and 2) be the generation of a numerical solution that does not map to a valid DF angle.
A simple estimation method has also found limited real time success in the past. The simple estimation method may function by evaluating all possible solutions that could result from one of the phase measurements. The phase measurement from the long baseline may be used as the basis for the estimation. For each of the possible DF solutions, the other phase measurements are estimated and compared to the actual measured phase values. The root mean square (RMS) of the difference may be calculated and compared for all the possible solutions. The solution with the smallest RMS distance between the estimated and measured phase values may be selected as the DF solution.
One advantage of the simple estimation method over the closed form method may result when there are possible numerical solutions calculated by the closed form method that do not generate valid DF solutions. These solutions would be discarded by the estimation method with the selection of the accurate DF solution being from the possibilities that provide valid DF solutions. This case may exists where the DF array may receive and attempt to process a signal of at a frequency below the maximum unambiguous frequency range of the array. The number of valid solutions in proportion to total solutions may be approximately equal to the ratio of maximum frequency to intercept frequency. For example, in an array with an unambiguous frequency range of 2-18 GHz (a standard frequency range of radar emitters), with a maximum frequency of 18 GHz, the array may produce a number of solutions 50% of which are valid at 9 GHz and 11% of which are valid at 2 GHz. At lower frequencies near 2 GHz, the estimation method may generate a more accurate DF solution at a lower SNR than would the closed form method.
One primary drawback of the simple estimation method may be the number of mathematical operations required and the resources required to accomplish the operations. For a standard nλ spacing 2n possible DF solutions may exist for each phase value of the long baseline pair. Five multiply operations, in addition to several other more simple operations, are required for each evaluation. Thus, for each possible solution, over 10n multiply operations as well as several other operations would be required. Next, a comparison of all 2n solutions is required to determine the best fit DF solution. An FPGA implementation of the estimation method would require extensive and costly component resources.
For each 1λ increase in spacing, an increase of 10 multiply operations is required. Much greater spacing of the antennas may be considered, however, current FPGA resources required and timing constraints would discourage implementation of such an algorithm for such an increase in spacing.
Therefore, a novel hybrid approach may be necessary to accurately calculate a DF angle at low SNRs from the electrical phase measurements taken by a linear interferometer with any baseline. This hybrid approach may comprise portions of the closed form techniques combined with estimation techniques to determine a very accurate DF solution from any RF frequency signal at all SNR with limited computational resources required.